PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On fundamental solutions of binary quadratic form equations

Volume 169 / 2015

Keith R. Matthews, John P. Robertson, Anitha Srinivasan Acta Arithmetica 169 (2015), 291-299 MSC: Primary 11A55, 11D09, 11D45. DOI: 10.4064/aa169-3-4


We show that, with suitable modification, the upper bound estimates of Stolt for the fundamental integer solutions of the Diophantine equation $Au^2+Buv+Cv^2=N$, where $A>0$, $N\not =0$ and $B^2-4AC$ is positive and nonsquare, in fact characterize the fundamental solutions. As a corollary, we get a corresponding result for the equation $u^2-dv^2=N$, where $d$ is positive and nonsquare, in which case the upper bound estimates were obtained by Nagell and Chebyshev.


  • Keith R. MatthewsDepartment of Mathematics
    University of Queensland
    Brisbane 4072, Australia
    Centre for Mathematics and its Applications
    Australian National University
    Canberra, ACT 0200, Australia
  • John P. RobertsonActuarial and Economic Services Division
    National Council on Compensation Insurance
    Boca Raton, FL 33487, U.S.A.
  • Anitha SrinivasanDepartment of Mathematics
    Saint Louis University – Madrid campus
    Avenida del Valle 34
    28003 Madrid, Spain

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image